If a person dyes his or her hair after highlighting it, he or she runs the risk of covering up the highlights. The best practice is to color or dye the hair first, then apply highlights.
When done by a professional, there is little chance of damage to a person's hair when applying color and highlights. Most professionals recommend, however, to complete the entire process at the same time. If one chooses to have highlights put in, then returns for an overall dye job, the highlights will become more subdued or disappear altogether. The only way to correct this is to have highlights applied again. This reapplication of highlights in a short time frame may damage the hair.